https://ntrs.nasa.gov/search.jsp?R=19700003070 2020-06-21T06:20:43+00:00Z

UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING

AND A F P L I E D S C I B J C E

I N S T I T U T E OF SOUND AND VIBRATION RESEARCH

ACOUSTICS GROUP

A COMPUTATIONAL STUDY OF ROTATIONAL N O I S E

By S.E. Wright and H.K. Tmna

I.S.V.R. Technical R e p o r t No. 15

May, 1969.

A u t h o r s : . As. S.E. Wright/

*I& ...............

CQ - G r o u p C h a i r m a n : ..... .. .... C . L . ' M o r f e y - for P.E. D o a k

H.K. Tanna

The work described i n t h i s report w a s sponsored by:-

Ministry of Technology, S t . Giles Court, London, W . C .2.

Mintech. PD/40/0 39/ADM

National Aeronautics and Space Administration, Washington D.C.

N.A.S.A. Grant NGR-52-025-002.

The work reported here i s a continuation of the investiBation

i n t o the study of ro t a t iona l noise reported e a r l i e r (I.S.V.R. Technical

Report No. 5($. The purpose of t h i s present report is t o give i n

graphical form the computed output of an extensive computational study

of ro t a t iona l noise.

output i n any way or discuss i t s implications ( see I.S.V.R. Technical

Report No. 14 ( 2 ) ) .

No attempt however i s made t o in t e rp re t the

The computation covers the properties of blade loading

harmonic radiat ion f o r a wide range of ro to r parameters, including

near f i e l d , d i s t r ibu ted loading both chord and span, and f o r t i p

speed i n excess of Mach one.

blade loading radiat ion, both simple and compound.

radiat ion is computed f o r an ensemble of blade loading harmonics

corresponding t o well-defined blade loading azimuth functions , similar t o those produced by blade s l ap and ro to r / s t a to r interact ions.

The study although designed f o r a par t icu lar ro tor (he l icopter ) , has

su f f i c i en t scope t o cover geometries of other rotor configurations.

The invest igat ion then considers composite

Final ly the

Contents

1. Describing the computation.

2. Defining the output.

3. Case schedule.

4. L i s t of f igures

1. Properties of blade loading harmonics

1.1 Fax f i e l d 1.2 Near f i e l d

2. Composite blade loading spec t ra

2.1 Simple B.L.H. addition 2.2 Continuous 3.L. spectrum 2.3 F l a t B.L. spectrum 2.4 B.L. azimuth functions

3. I l l u s t r a t ions .

Page

1

2

' 7

14

1. Describing the computation

The invest igat ion has been designed t o e s t ab l i sh the propert ies of

ro t a t iona l noise over as wide a range of parameters as coaputing t i m e

would allow.

speed computer i s of the order of s ix seconds per harmonic per f i e l d

Bearing i n mind t h a t t he ty-pical computing time on a high . .

point, then each computed case m u s t be an attempt t o achieve maximurn

information for minimum computing time.

been an advantage t o increase the spectrum or polar resolut ion by at

l e a s t a fac tor of two or have decreased the integrat ion i n t e r v a l by a t

I n some cases it would have

l e a s t the same margin, but of course the computing time and therefore

the cost would have doubled.

1.1 Standard case

A s a consequence of the number of parameters involved, a standard

case has been adopted such t h a t the sound pressure i s calculated for a

standard s e t of parameters (those of a ty-pical helicopter r o t o r ) and then

deviations i n rad ia t ion computed for a range of parameter changes taken

one a t a time; it i s of course computationally prohibi t ive t o cover

a l l combinations of ro tor variables. However, some paxameter reduction

is possible; for instance, the sound pressure harmonics ( m ) a re plot ted

i n t e r m s of the mB parameter, as m and B (blade number) a r e indis-

t inguishable mathematically, even f o r d i s t r ibu t ive loading - e.g. if

B = 4 and m = 1 or B = 1 and m = 4

the same.

of t he number of blades providing the t o t a l ari thmetic blade loading i s

the sound pressure l e v e l (S.P.L.) i s

The spectrum envelope, both i n shape and l e v e l i s independent

- 1 -

the same. Only spectrum l eve l s of mB numbers corresponding t o multiples

of B have physical significance. Similarly the ro to r frequency ( N ) and

the e f fec t ive radius loading point

e f fec t ive Mach number parameter (Me) .

(re) can be p lo t ted i n the form of an

The values fo r the standard case

are given i n f ig . 3.1.

1.2 Computation programme

The computer programme used for the study computes the ordered sound

pressure spectrum re la ted t o the blade passage frequency a t any observation

posit ion, including the near f i e l d . Both steady and f luctuat ing l i f t

radiat ions are calculated i n the form of individual blade loading harmonic

radiations. The programme has the f a c i l i t y t o compute d i s t r ibu t ive span-

w i s e loading, but i s r e s t r i c t ed t o rectangular dis t r ibut ions i n chord pro-

f i l e .

Report No. 13 3) .

F u l l de t a i l s of t he programme a re given i n 1 .S .V.R. Technical

2. Defining the output

2 .1 Single blade loading harmonics

For the study of blade loading harmonic (B.L.H.) properties, the t o t a l

l i f t LOT

number of blades, by adjusting the l i f t per blade accordingly.

the B.L.H. coeff ic ient

metic B.L.H. amplitude LST

of t h e B.L.H. order s or blade number B.

on the ro tor i s kept constant a t 12,000 l b s i r respec t ive of t he

By making

( a s ) equal t o unity throughout, the t o t a l ar i th-

i s a lso maintained a t 12,000 lbs , i r respect ive

Four of t h e parameters l i s t e d i n the standard case are l i nea r para-

- 2 -

meters, i . e . the.S.P.L. i s d i r ec t ly re la ted t o t h e i r value.

t o t a l l i f t LOT and B.L.H. coeff ic ient as% are d i r ec t ly proportional t o

the sound pressure and the remaining two, ro tor radius

blade aspect r a t i o i s constant) and far f i e l d observer distance

inversely proportional t o the sound pressure.

t o compute a range of these values. For example, t o correct f o r a rotor

having half the t o t a l t h rus t (-6 dB), a B.L.H. coeff ic ient of a tenth

The f i r s t two,

r (providing the

R are

Obviously there i s no need

(-20 dB), a ro to r radius of one ha l f having the same t i p speed (+ 6 dB) and

an observer a t h i r d of the distance (+ 10 dB), then a t o t a l of 10 dB w i l l

have t o be subtracted from the general spectrum level . The remaining para-

meters a re not simple mul t ip l ie rs , they a f f ec t the spectrum shape as w e l l

as the general l eve l ; these a re the blade force angle B , ef fec t ive t i p

Mach number M span d is t r ibu t ion , and chord width a. Therefore the e '

e f fec ts of the above parameters a re computed over a l imited range of

p rac t i ca l i n t e r e s t .

Further, the sound pressure spectrum i s a function of observer

elevation angle f o r s ing le B.L.H. radiat ions and depends on both elevation

and azimuth angles for composite B.L. radiat ions.

decided t o define a l l output a t one f ixed point f o r mB spectrums, i . e . ,

azimuth angle

ro tor plane) .

plan were then positioned so as to contain the above coordinates.

observer distance R i n each case is 300 f t from the centre of the ro tor

(see f i g . 3.2).

It w a s therefore

0 = 0' (from t a i l ) and elevation angle

Polar p lo ts corresponding t o the polar elevation and polar

CT = -30' (below

The

In the case of near f i e l d calculations, where the S.P.L. is not

d i r ec t ly r e l a t ed t o the observer distance, the addi t ional e f f ec t s of mB

- 3 -

number, span d is t r ibu t ion , ro to r speed and ro tor radius are a l s o computed.

The various span d is t r ibu t ions used i n the invest igat ion are defined i n

f i g . 3.3, and are calculated f o r a t o t a l l i f t of 3000 lbs per blade.

2.2 Continuous B.L. Spectrums

The addi t ional parameters for the f la t B.L. spectrum study are defined

as a continuous spectrum of B.L.H. from s = 1-t 200 w i t h zero B.L.H. fa l l -

off ( a s = 1 for a l l s values) and zero B.L.H. phase 4s = 0'. For

computational convenience, the B.L.H. amplitude Ls i s kept constant

a t 3000 l b s per blade i r respec t ive of t he blade number used.

tha t t o correct fo r a standard t o t a l ari thmetic B.L. amplitude

12,000 lbs , 20 log(B/h)

This means

Lsr of

w i l l have t o be subtracted from the computed leve l ,

e.g. if the computational blade number B = 12 then the correction i s

-10 dB.

The phase 4, of the B.L.H. f o r the random phase study, i s achieved

for

(a) Random polar i ty , by assigning random polar i ty t o the cosine B.L.

component and making the s ine component zero at each radial s t a t ion , the

po la r i t i e s for a given harmonic being ident ica l a t each of these s ta t ions .

(b) Random phase, as above but both s ine and cosine components having

random polar i ty .

( c ) Uncorrelated phase. Here both s ine and cosine components have random

polar i ty but with zero correlat ion between radial s ta t ions .

The 6 dB per octave B.L. spectrum is defined as a continuous B.L.

spectrum with a = 0.1 fo r s = 1, and then progressive values of a

reducing a t the rate of 6 dB per octave i n

S S

s.

2.3 B,L. azimuth functions

The blade loading azimuth functions used i n t h e study are i l l u s t r a t e d . .

i n f i g . 3.4.

per blade revolution

The standard B.L. function is a s ingle rectangular excursion

E = 1, having a load s o l i d i t y p = 1%, or an excur-

sion width

The height of t he function, or load change AL,

1800 lbs per blade, which when expressed as a percentage of the standard

W of 1% of the effect ive d i sc s o l i d i t y , i.e. p = W/2are.

i s 50 l b s per i n or

steady load of 3000 lbs per blade, i s 60%. A load change AL of 1800 lbs

per blade corresponds t o a maximum blade loading amplitude Ls max ( a t

1017 s numbers fo r rectangular and hal f cosine functions and a t medium

s numbers for f u l l s ine function) of 1 l b per i n o r 36 l b s per blade.

For computing purposes, t h i s par t icu lar value of Ls m a x = 36 lbs

per blade i s kept constant throughout the azimuth B.L. study.

if the number of function excursions E, or the load s o l i d i t y

example doubled, then the load change i s e f fec t ive ly halved, and 6 dB

Therefore

i s for p

would have t o be added t o the computed spectrum l e v e l t o correct fo r a

standard load change of 1800 lbs per blade.

As i n the case for the f la t B.L. study, the t o t a l ari thmetic B.L.

i s t h a t of one blade times the blade number used i n the computation.

Therefore, i f a radiat ion spectrum is required fo r a blade number other

than t h a t used i n the computation, then a subtraction of 20 log B/Br

w i l l have t o be made from the general spectrum l eve l , where

computational blade number and Br i s the required blade number.

Two fur ther parameters which e f f e c t the computed S.P.L. a r e the

dB

B is the

azimuth and span integrat ion interval . These parameters a r e discussed

- 5 -

fully i n I.S.V.R. Technical Report

the accuracy of t he computation is

13. It is su f f i c i en t t o say here t h a t

a function of the integrat ion in te rva ls

used, ~m5 ;Poi- econoaic reasons, these in t e rva l s were adjusted t o give a

reasonable accuracy fo r a r e a l i s t i c computing time.

A summary o f the computed output is given i n the l ist of figures and

each computed case is f u l l y defined i n the case schedule.

- 6 -

. M

e n f f i o

X I

..

E-r E 3

--7

~a

$.1 E m w - m u a 4 6

0 0 0

0 0 ???a 0 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 c u c u 0 0 0 c u c u c u c u c u c u c u c u f f f f f f f f f f

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M M M M M M M M M M ~ M M M M M M M M M ~ M M

o o o o o o o u o o o o o o o o o o o o o o o u3u3u3u3u3u3u3u3u3Ofu3u3u3u3u3u3u3wu3uo3 cu cu

f f f f f f f f f f f f f r l r l r l d d r l d r l r l r l

0 0 0 0 0 0 0 0 0 0 L n I n ~ L n L n l n L n L n L n L n

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

- 7 -

E H -3 -,a

o o o v o o o v u 0 0 0 LnLnLn LnLnLnLnLn?yLny

c u C U d 0 0 c u c u c u c u c u ~ c u c u f ~ f f f f f ~ f ~ 0 0 0 0 0 0 0 d 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 *

0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 w w w w w w ~ w w o f w w w w w w ~ w w w o f w w w w w w w w o CU cu

0 0 0 0 0 0 0 0 0 0 I n L n L n L n I n L n L n l A L n L n

- 8 -

rn

ffiffi

X 4 0 p t a m

0 0 0 0 L n L n L n L n

* * ~ 0 0 0 0 0 0 0 0 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ooocucucucucucucucucucucucuowcu~wcuwcuwcuwcuwcuw

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f w \ o w w w \ c ) w w w \ c ) w \ c ) w w w w w \ c ) ~ \ c ) \ o w w w ~ w w w w cu

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LnLnLnLnlnLnLnLnLnLn rlrlrl

- 9 -

R R H 3 - \a

R m m O Q F r HE;

z a a

X t i d m m * a

R 0

I &

M M

0 0

-0

0 0 rlo r i m

“0 rloo r l r l

0 0 0 0 0000 cucucucu

0 0 0 0 (N(Ncuc\ I

n n n n 0 0 0 0

R 2 H 3 -4

I

m a

0 0 rl

- 11 -

f3 8 3 ~a

-----%

E 5 m

I 0 0 L n l n L n

o r l o r l o r l = = *o eo 0 0

f3

4 0 = ffi w N

3 f3 m = a 8

R

Fi 0 = ffi w N

A

0 0

0 rl

9 9 0 0

- L c c

cucucucucucucucu cu

co f c u M

L L

L L

- c

L L

e e

c c

3

cu

L c

L L

c L

13 -

L - L L L - L L c L

L L C L L L - L L e

- L - L L L L e L L

L - L L

L L - L

L L L e

L c

L L

c L

L -

L L

e c e - - L

- L

L L - L

- L

L L

3 L n u3 3 3 f c u c u cu

4. L i s t of f igures

1 Properties of blade loading harmonics

( f igure numbers are shown i n the columns)

1.1 Far f i e l d

Effect of span d i s t r ibu t ion mB f a l l o f f polar elevation-O.3%

- con s t an t

-zero l i f t

-10%

-tr iangular

Effect o f chord width mB f a l l o f f

Effect of force angle mB f a l l o f f polar elevation - 0'

- 6' - 24'

.Effect of Mach number mB f a l l o f f polar elevation - 0.25

- 0.5

- 1.25 - 0.75

s =o

1 2 3% 4 5 6

7

8 9 3" 10

11 12

13 14

3"

s=12

15

17'

19 20

2 1

22 23 17" 24

25 26 17" 27 28

16

18

s =48

29 30 31' 32 33 34

35

36 37 31" 38

39 40 31* 4 1 42

* STD CASE.

1.2 Near f i e l d

Effect of span dis t r ibut ionfobserver distance mE3 = 4 1

Effect of mB number observer distance 2 6 16 polar elevation - m~ = 4 3

- m ~ = 6 7 - m B = 1 2 8 -DIB=I-~ 9

Effect of ro tor speed observer distance - mS 4 4 - m ~ = 6 10 - m B = 1 2 11 - m ~ = 1 8 12

S=O s=12 s=48 Effect of ro to r radius observer distance - mB = 4 5

- & = 6 13 - m B = 1 2 1 4 - m = 1 8 15

2 Composite blade loading spectra

mB FALLOFF POLAR

'IGf' E U V A PLAN RES. RES. 2.1 Simple B.L.H. addition s12 + s24 1 2 3

2.2 Continuous B.L. spectrum

Effect of B.L.H. f a l l o f f f la t spectrum 1" 2* 3" 5* (inphase B.L.H. ) 6 dB/octave 1 2 4 6

Effect of B.L.H. phase random polar i ty 7 8 i o ( f l a t B.L. spectrum) random phase 7 9 1 1

7 inphase 7* 3* 5*

uncorrelated phase

2.3 F l a t B.L. spectrum

Effect of span d is t r ibu t ion

Effect of chord width

Effect of force angle

Effect of Mach number

Effect of observer distance

Effect of number of B.L.H.

0.3% 10% constant zero l i f t 1" 16" 64 '' O0 6 O

24' 0.25 0.5 0 - 75 1.0 1.25 300 120'

60 t 30 ' 26' 1 -+ 100 1 -f 200

1 2 1* 2* 1 2 1 2

11 12 11" 12* 11 12 17 18 17" i8* 17 18 23 24 23" 24* 23 24 23 24 23 24 33* 33 33 33

3 7 4* 8" 5 9 6 io

13 15 4* 8%

1 4 16 19 2 1

20 22 25 29

26 30 27 31

4" 8"

4* 89

28 32

34 38 4* 8*

35 39 36 40 37 4 1

42 42

mB FALLOFF POLAR

2.4 'B.L. azimuth functions

Effect of load s o l i d i t y 1% 10% 50%

Effect of number of excursions 1 4 16

Effect of type of function rectangular half cosine f u l l s ine

3 I l l u s t r a t ions

The standard case 3.1

Low 'IGH ELEVA PLAN RES. RES.

1" 2" 1 2 1 2 9" 10" 9 10 9 10

15 16 15 * 15 16

3" 6% 4 7 5 8 3% 6% 11 13 12 14 17" 20% 18 21 . 19 22

Observer def in i t ion around ro tor 3.2

Span d is t r ibu t ion def ini t ions 3.3

B.L. azimuth functions 3.4

- 16 -

LIST OF SYMBOLS AND ABBREVIATIONS

a

B

B.L.

B.L.H.

E

F /F

LO

LS

LOT

LST

m

Me

N/F

N

r

r

R

e

T

S

S.P.L.

w

S

B

AL

6

P

a

CT

4s

blade chord width

blade number

blade loading

blade loading harmonic

number of blade loading function excursions

f a r f i e l d

steady l i f t per blade

t o t a l steady lift LOT = LOB

S harmonic blade loading smplitude

t o t a l ar i thmetic blade loading amplitude of order S, LST = LsB

sound pres sure harmonic number

e f fec t ive Mach number

ro tor frequency Hz

near f i e l d

ef f e c t ive rotor radius

rotor t i p radius

observer dist&ce from ro to r centre,

blade

sound

blade

blade

force

loading harmoni c number

2 pressure l e v e l dB r e f . 0.0002 dynes/cm

loading function width

loading coefficient a = -

(or ef fec t ive blade l i f t ) angle

LS

Lo

load change

observer azimuth angle ( t a i l

load s o l i d i t y p = W/2nre

observer elevation angle ( ro to r plane CT = 0')

blade loading harmonic phase, order S.

6 = O o )

- 17 -

REFERENCES

1. WRIGHT, S.E. 1968. I.S.V.R. Technical Report No. 5. J. Sound Vib. (1969) 9 (2 ) . Sound radiat ion from a l i f t i n g ro tor generated by asymmetric disc loading.

2. WRIGHT, S.E. 1969. I.S.V.R. Technical Report No. 14. Theoreti c a l study of ro t a t iona l noise.

3. TANNA, H.K. 1968. I.S.V.R. Technical Report No. 13. Computer programme fo r the prediction of ro ta t iona l noise, due t o f luctuat ing loading on rotor blades.

- 18 -

B.L.H. PROPERTIES t o t a l l i f t Lo, = 1 2 9 0 0 1 b s - - B L o

B.L.H. coef f i c ien t o<s= 1 -- - Ls L O

Sth 8.L.H. ampl i tude LS = 'Var iab le ( f n of B )

t o t a l ari thmetic B.L.H. ampl i tude LST = 12000 I b s b l a d e f o r c e an'gle ' p = 6"

ef fect ive t i p Mach No-. M e = 0.5

ef fect ive t i p r a d i u s r e = 2 4 f t

t i p r a d i u s rT = 3 0 f t

r o t a t i o n a l frequency N = 3-7 Hz

span d i s t r i bu t ion D i s t = - Rectangu lar 10

cho rd w i d t h a = 1 6 i n

FLAT BLADE LOADING SPECTRUM

- as B. L. H. p r o p e r t i e s B,'L.H. s p e c t r u m range S = 1-200

B. L .H . coe f f i c i en t o(s = 1

B . L . H . p h a s e 4s = 0"

SthB . L . H. a m p l i t u d e LS = 3000 Ibs /b lade o r 83.3 l b s / i n

LST = Var iab le ( f n of B )

B . L . A Z I M U T H FUNCTIONS as B. L.H. proper t ies

Type of funct ion f n = Rectangu lar

toad s o l i d i t y ? = 10/0 Number of excursions E = 1

Ls Max = 1 Ib/ in or 36 l b s / b l a d e

load change - AL L O

= 60 "/" or AL = 50 lbs/ in

Fi.g 3.1. The standard c a s e s

0

0

Fig. 3.2 .ObSQrVQr definition around rotor.

I

I

Impulsive 0 *3%

t L o = 83-3 lbs / in

STD. case 10 O/O

Constant looo/o

Triangular

Zero lift I I I I J

15'

L 0 = 16.67 lbs / in t Lo = 8.33 Ibs/in

Lo= 8.33 l b s / i n

Fig. 3.3 Span distribution dafinitions

e = 0" I

.'t f n = Rectangular f n = Half cosine

Type of function E = l , r = l o / "

f =lo /" f = lo"/"

Load solidity f n = r e c t , E =

fn = F u l l sine

1

E = 1 E = 4 E = 16

Number of excursions f n = r e c t , f = 1 ' / 0

Fig. 3.4 B.L. A z i m u t h func t i ons

P cn Y

Y

I I

100

s.F! L. (dB1

80

60

40

20

0

2 0

40

60

e a

1oc

goo

Fig.1-1.2 E f f e c t of d i s t r i b u t i o n fl

Rec t . 0.3% S = O

100 s.f? L. (dB)

80

6C

40

2 c

0

2 0

4 0

60

8C

1 oc

9 0"

r

11 2

3 O0

Fig 1-1-3 Ef fect of span d i s t r i b u t i o n , . Rect. 10% (Std. case) S =O

100 SPL

( d B) 80

60

4 0

20

0

20

4 0

60

80

100

90"

1 0"

Case 116

goo

Fig. 1.1.4 E f f e c t of s p a n d i s t r i b u t i o n Dis t r ibut ion =const . S =O

100 S.P. I . (dB1

80

60

20

0

20

40

60

80

100

90

Fig. 1 . 1 5 -E f fec t of d i s t r i b u t i o n

Tr iangu lar S =O

. .

F i g . 1.1-6 Effect of distribution , zQf-0. lift S = 0 .

3

rc 0

v

4 d m

x + 4

Q) 0

Q) 0

c-

P

c- 0 c

rn E 0 N

6 0 I

I f

b * d

I I 7

m

N .- 0) c

w co

N

100

s .P.L (dB1

6C

4t

2t

t

2t

4r

6(

8(

lo(

0

11 9

-90"

Fig.1.1.9.Effact of force angle p = 0" s = 0

f" 0"

Case 120

0" Fig. 1.1.10 Effect of force angle (3 = 24' s = 0

m E

- 90"

Fig. 14.12 E f f e c t of Mach no. Me=.25, S = O

100 S .P .L .

(dB 1

80

60

4c

2c

0

20

4c

6C

8C

1 oc

GaSQ 1 1 4

1 I 1 I I I I I I I I , I 0 4.- 0 0 0 0 0

h) 2 f q 'I" 0 OD (D -3

# Y

U

[D m

N m

OD N

8

0 hl

(D F

cv 'c

aD

U

0

U U

at E

cu I t

VI

(P

0

0 m i

II

b

Y- O

i

120 S.FIL. (dB)

100

80

so

40

20

0

20

4 0

60

80

109

120

t" 0

132 (Std . case 1

Fig.1.1.17 E f fec t of d i st r ibu t ion 10% (s td . .case S = 12

Fig.l.l.18 Ef fec t of span d i s t r i b u t i o n Constant S =12. >

138

I

100

s. P. L ( d B )

80

60

LC

2c

0

20

4c

61

8(

101

Case 136 A

Fig. 1.1420 Effmt of distribution, zero l i f t S =I2

c

2

2 ..

0

c cv c-

ui Q, ui ru 0

\ 630 ‘i

u ui

5

/

0 0’

U U

0 U

<D <*)

N m

aD N

U N

m E

0 r4

(D c

c\I c

a0

U

a3 (v c - a0 N c

.- (v t-

J I I 0 0 0 0 0 0 . 0

N A - 0 03 co * (v

vi- t- c IXg

e

39

Fig.l.l.23 Ef fec t of force angle f l =O" S=12.

120

s .?. L (dB)

100

80

60

40

20

0

20

40

60

80

100

120

t"* 0"

Case 140

Fig.l.1.24 EffQct of force angle. p =. 24'. s ,I2 .

3 30

E m E

N r-

oo Lo

U (D

0 Lo

(D v,

N m

00 4

U U

0 U

1D cr)

N m

aD N

zt N

0 N

1D

N - Q)

-.Y

12( s.P.L (dB 1

lot

81

6t

4c

2C

C

2c

4(

6(

8(

lo(

12c

0"

133

. Fig.1.4.26 E f f m t of Mach no. Me = 0-25, S 4 2 .

120 s .P.L

( d 8 1

1 oc

80

6C

40

20

0

20

40

60

80

100

120

I d

4

Fig.1.1.27 Ef fsc t of Mach no. Me = 0.75 S -12.

0 N c

I 0 0 0 0 0 0 0

( 8 P ) '1'd'S 0 a0 w - N c-

N -

0 0 c

0 co

0 m

0 w

0 m

0 (v

0 P

'%--

0

P

r- cir G-

Case 157

J

but ion 8

90’ V

120 s.f? L.

( d B )

100

80

60

4c

2c

c

2c

4c

6(

8(

100

12c

Case ,156

t i o n

-90"

Case 158

Case 156

Fig.1.1-34 Ef fact of. distribution, zero lift .

A

S = 48

0 In b

CI e 4 c

- - - 2.

0 0 c-

0 m

0 oa

8 IU CD L

0 Jz

Y-

o 0 t n .

I I I 1 I I I I 0 0 0 0 0 0

0 a0 to -3 N 8 (v

c c

0 c3

0 N

1 I 1 I I

0 0 hl s c

0 0 0 0 co co -a hl

Bp ‘ l a - s

Y-

O

\

120 SPL (dB1

lo0

80

60

40

20

0

20

60

60

80

100

1 20

4 d

m -3

7 - c

I I 1 1 0 0 0 0 0 0 8 co * N

0 N - P

Q E 0 (v’ P

0 c P

0 0 P

0 CD

0 a0

Q 0 m

I

.;I h

OD v rn

I I

0 !3 L

0

+- 0

120 S.#?L. I d B )

100

80

60

40

20

0

20

LO

60

so

100

120

I I

I 0 0 0. 0 0 0 ( v . 0, a3 U N

J -

q - 0 m--

.-

a m

0 0 cr)

0 0 (v

0

0 z 0 m 0 r- 0 Go

Q m

0 9

0 Cr)

0 hl

I s2

c (II @) z

o) LL .-

S 120

100

80

s.f? L. I d B1

60

40

20

a

2(

I (

6C

8C

1 O(

12( -

0

Fig.12.3 Near field - effect of mB number O0 S= 0 mB = 4 polar elevation .

cn rsE! b CD c-

4

4

.-

.- CD

0, u) rp 0

I I I I I i I 1 I I I I I I

0 0 0 0 0 * cv 0 Go (D 0 j-0

.- c , m a c u - c Ui,

0 II

cn

L

4

L

0 0

Y-

O

m E

0 0 0

0 0 N

0 ro P

8 0 a0 0 PI

0 (D

0 In

0

0 0

0 OJ

v) c5

U c Y

m E c 0

c c tY

(0

cu . r-

s .P. L ( dB1

120

100 S.P L. (de l

80

60

40

za

0

2c

4c

6(

8C

1 O(

12c

(D I t

m E

0 0 cu

0 v3 0 e 0 cp

0 Ln

0 U

0 m

0 cu

9

U o x 4n t 0 0 .cI

L * 0

L (0

0 'c-

0

-.

a m s s Q: s

-. 9 ..

CI)

o o - -

v,

0 c'?

I

6 F-

$

00 cy

11

m E . n

cu T--

II

m

u- 0

4 V Q,

Q,

u- \c

I

. m 11.

t

1- a

I 1 I I I I O i-, 0 QI) a zt 2 .-

0 hl

0 0 0 0 0 0 a P

0 0 m

0 0 .-

c- .w u- Y

+ ul .- n

0 P

0 P

v)

0

UI

m I t

E

u) 3

U co L

L

c,

L

.-

0 0

Y-

O

4 U Q,

QJ

w- 'c

I 0 0 0 0 0 0

(D U 0 a0 a I

0 P

(v - s - -I- - d m 'U Cn-

0

0 c

* 0

0

.I

N I

O b 0 . m m I

I1 I I

b z

a ag Co .-

0 (v

0 0 cr)

0 0 P

- Y \c CI

0 . - 'w

tn .- n

0 P

u! 0

c-

0 o o tD e

m

0 00

0 (D

0 hl c

0 I

0 0 m

0 0 hl

0 m - c w c Y

0 3 ; - n 0 .- 0 Qa

0 00

0 rz

0 LD

0 In

0 G

0 0

0 hl

0 .-

cu T

131 .- L i

UJ cz 7 . U

.

Q

a v)

0 0

c 0 e U 7 3 a

.-

I J

Y

J

b d -u;

t m Q

L m 0. Q

-

-

-3 cu v) + (v c

v)

c 0

P P

.- w .-

II I

x

I i

x

%

X

I m U co

0 0

41 N

N N

- n 0 N m

h, L

"C

L-

-------

I

0 . c a c 4

3 0 3 21: 33 C 0 0

.-

cn .- LL

E .

8 3 L .c.'

CL

0 0

c

0 e _p

I

u 0

L

0

e-

E

0

0 I t

cb

E 0 TI 6 Iu L

1

a

0

0

r Q

E e 4J

E 0 U t (0 L

I

0 0

cb -

Ln m N .

U m N

-

E

c9

d

---T

X

I X

c

a

a-

Ln m (v

m (v

I 0 0 0 0 0 0

0 a0 v, * hl N .---- I .-

Q f

9 0"

S

Fig 2.3.3. Flat B.L. spectrum Dist.5 0.3°/0. Polar . ~ I ~ v a t i o n Q = Qo

90"

-90"

Fig. 2.3.4. Flat B.L.speetrurn, std. case, Polar elevation 8 = 0"

S.? L. dB

Fig. 2.3.5 F l a t B.L. spec t rum D i s t = constant P o l a r e l e v a t i o n e= 0"

_ .

Fig. 2.3.6. Flat 8. L. spectrum, Dist . = z ~ r o l i f t . Polar elevation 0 = 8"

0

0 Case 237A

Fig. 2.3.7. Flat 6. L .spectrum, Dist. = RQct . 0.3% Polar plan G = -30"

F i g . 2 . 3 . 8 F l a t B.L. Spectrum std . case Po lar .plan = -30"

Case 2 3 6 A 0"

180" . spectrum, Dist.= const. Polar plan

180"

F i g , 2.3.10 F l a t .L. s p e c t r u m . Dis t = zero I i f t . Po la r p l a n 6= -30"

m

Cr, M

Fi.g. 2.3.13 F l a t B.L. s p e c t r u m a = l ” p o l a r e leva t i on

90" t

Case 232

11

Fig. 2.3.14. Flat 0 . L .spectrum . a = 64 . Polar elevation . e= 0"

I

ig. 2. 3.15. Flat 8. L spectrum. a = I' Polar plan. ~ = - 3 0 '

140

120

S.P.L dB

80

60

40

20

0

20

40

60

80

100

.120

140

Fig.

- 8 Case 232 A

180"

2.3.16.

= 12 48 24

Flat B.L. spectrum . a = 64" Polar plan G = 30"

U cv 0

U cv

0

1 1 I I 0 0 0 0 0

N - 1 co U cv 0

00 0 %-- i g 2

st (v

N N

0 N

U .- gl E

N c

0 .-

og

U

N

0

S.P. dB

Case 2.29

0"

I 96

9 Flat B.L. spectrum (3 = 0" . Polar elevation 8 = 0"

9 0"

Case 230

- 90"

Fig, 2.3.20 F l a t B.L. spec t rum / 3=24" Polar e leva t i on e = O 0

140 s .P.L

dB

100

8C

60

0

2c

4 c

60

1

1 oc

121

Case 229A

90"

141 180"

Fig. 2.3.21 . Flat f3.L spectrum (3 = 0" . Polar plan ci"= - 3O0

2 3 0 A

I2 24 4

L

Q

0 0 0 0 0 hl 0 aD (D 2, c- c

...- -3 N

N N

0 N

511

e r-

m E

N c

0 c-

CD

0

25

- 90,

Fig. 2 - 3 . 2 5 F l a t B.L.spectrum Me=0.25. Polar e levat ion e = O o

s. P. L dB

Fig. 2.3.26. Flat B. L spcctrum . MQ = 0.75 . Polar QIQvation 8 = 0"

F i g . 2-3.27 F la t B.L. spec t rum M e = l . O Polar e levat ion (Y- 0"

Fig. 2-3-28 F l a t B.L. spec t rum Me = 1-25 Po la r e leva t ion B= 0"

s .P. L dB

Fig. 2.3.30. Fiat B.L spectrum Me = 0.75 . Polar plan c= -30"

1 i o S.P.L

dB 120

100

80

60

4 0

20

0

20

40

6C

8C

1oc

120

14C

I

- 0 Case 227A

180'

Fig. 2.3.31 . Flat B.L spQctrurn . Me = 1.0 . Polar plan G = -38"

180"

I I 1 1 0 0 Q -3 N 0

J

Case 248

Fig. 2.3 .34 Fla t B.L. spectrum R =l20' Polar e l e v a t i o n e= 0"

Fig. 2 . 3 . 3 5 F l a t B.L. spec t rum R =60' Po la r e l e v a t i o n e = O o

160 s .P.C

d B I

120

1 oc

8C

6C

4c

2(

0

2(

4c

6l

8(

101

12(

1 4 (

16 ( 90"

Fig. 2 . 3 . 3 6 .

Case 248

1 8. L . spectrum . R 3 0 . Polar etwation 8. = 0"

1LO s . P.L dB

120

100

80

60

40

20

0

2 0

4 0

60

8C

1oc

12c

i 4 a

Fig. 2

---L e Case 248

I

3.38 Flat B. L spectrum , R = 12Q . Polar plan . G= -30"

0"

SP (d B

180"

Fig. 2 - 3 . 39 F l a t B.L. s p e c t r u m R = 60' Polar plan 6=-30°

12 24 -48

180'

F i g . 2 - 3 . 4 0 Flat 8 L s p e c t r u m R = 30' P o l a r p l a n 6=-30°

160 S.P.L

dB

120

100

80

60

SO

20

0

2c

4C

66

8C

100

126

i 4 c

16C

- 0

30" I

Fig.' 2.3 41. Flat B.L spectrum . R = 26 . Polar plan . G = - 30'

I I I I 0 0 0 0 0 0 0

c cu 0 U cv

0 U hl

0 cv N

0 0 cu

0 (P - 0 2.

0 s

0 N .-

m E

0 e

0 ae,

0 CD

0 U

0 (v

0

E 3 L +J V 0 n cn d

m c, a L CY

M

in LL

P,

c\i .-

8 P * 1 ' d ' S

0) a0 P

a- a0 c

b a0 c

Q, VI td u

: I

r ' t

'* I

I

I

I I

j f I I

3 h

u) a, L

Lo co

0 Lo

U .-

N U

-e u a,

%- \c

0 m

U (v

' 0 \ 0 0 m

1

0 In

cj -a

0 m

0 hl

0 t-

0

Case 192

214-3 Azimuth functions polar czlwation

S

Fig. 2.4.4 Azimuth functions - = 10% polar czlovation CY = 0'

dB

Case 194

Fig 2 - 4 5 Azimuth functions - (3=50% polar c2levation CY = GO

Fig. 2.4.6 Azimuth functions - f = 1% polar plan, 6 = :30°

8C

S.P.L WB)

6C

40

Case 191

0"

Fig. 2-4.8 Azimuth functions - r=5o0/0 polar plan, cr=--30°

v) Q, t

3 0 -.I

n

w

v) t 0 v) L 3 W X a,

0

t Q>

U

.-

rc

E 3 c

0 %-

+ V a,

a, w- rc.

I

v) c 0 4 W c 3

.-

9-

I: c, z .- N

-I < ai 07 4- cu 0)

LL .-

0 0 F

ar UI rd 0.

1 oc S.P.L

d 0 80

60

4c

2c

4C

ca'se 195

Fig. 2-4-11 Azimuth functions - E = 4 polar ebvation €Y= 0"

t Fig. 2-4-12 Azimuth functions - E=16

polar Qlavation 8. = 0

Case 195

== 12 24. 40

I 100'

s. P. L (dB 1

80

60

40

20

0

20

40

60

80

100

m

Fig.2.4.14 Azimuth functions - E=16 polar plan G = -30" .

- -a N . 0 -a N

m m N

01 m (d u

b, Q >, 4-J

Y-

o

v

x x - 1

I I I I II f I

.- o x 0) e In i ' x

\ x

I x

I i \

I X

I, x

1 x

I \ x

\ x

\ z x

.- 0 +J V c 3 Y-

9 0" 120

SPL ( d 8 )

100

8c

6C

4c

2c

0

2(

4(

61

81

101

121 - 0"

Fig.2.4-I7 Azimuth functions fn = r e c t . Polar elev. 0'= 0"

120 sf? L. (dB1

100

80

60

40

20

0

20

40

60

80

100

120

Fig.2.4.18 Azimuth functions f n =hal f cosine polar elev. @ = O "

120

10.0

80

4C

2c

4f

6C

8C

1oc

12c

1.20

100 s.f? L.

. ( d B )

. 80

60 T

40

20

0

20

4c

60

8C

1 oc

121

C a s e 216

F i g 2.4.21.Azimuth functions fn = half polar plan CT

cosine = -30"

Case 247

muth functions fn= fu l I s i n e , Polar plan o-=-30°